EASY
AS and A Level
IMPORTANT
Earn 100

Describe, in words, the locus represented by the following.
arg(z)=5π12

Important Questions on Complex Numbers

MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2
On an Argand diagram, sketch the following locus. Shade any region where it is needed.
|z-(2+i)|=|z-(4+3i)|.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2
On an Argand diagram, sketch the following locus. Shade any region where it is needed.
arg(z+3i)=-π3.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2
On an Argand diagram, sketch the following locus. Shade any region where it is needed.
|z+4-5i|⩽2.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2
On an Argand diagram, sketch the following locus. Shade any regions where it is needed.
|z-2i|⩽|z-4|.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 3
On a single Argand diagram, sketch the loci |z|=4 and |z+2|=|z-4|.Hence, determine complex number that satisfy both loci, giving your answer in Cartesian form.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 4
On an Argand diagram, sketch the locus |z|=|z+8i|. Find the Cartesian equation of this locus.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 5
Sketch the locus |z-(3-6i)|=3 on an Argand diagram. Write down the Cartesian equation of this locus.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 6
Sketch the loci arg(z+4+2i)=5π6 and |z-5 i|=4 on an Argand diagram. Determine whether or not there is a complex number, z, that satisfies both loci.